Applications and Misapplications of the Channel-Capture Formalism of Direct Neutron Capture

Abstract

We discuss the channel-capture approximation of slow neutron direct-capture theory. We show that this approximation gives a generally good representation of the neutron capture cross sections for several electric dipole transitions in a broad range of nuclides from A = 9 to A = 136; these are mostly near-spherical nuclei. Despite this body of agreement, we examine the accuracy we can expect from the simple channel-capture theory. Comparison with calculations of the potential-capture cross section from physically more realistic optical model calculations shows that, in general, the channel-capture cross section can be up to ≈40% in error. In cases where the expected channel-capture cross section is much smaller than the “hard-sphere” capture cross-section estimate, the disagreement with potential capture can be much worse than this. Also, in these cases, compound-nucleus capture can be of comparable or greater magnitude. These effects have been shown to completely undermine recent attempts to determine nuclear interaction radii for targets, such as ¹²C and ⁹Be, by application of the channel-capture formula to capture cross-section data.

Research sponsored in part by the U.S. Department of Energy under Contract No. DE-AC05-840R21400 with the Martin Marietta energy Systems, Inc.

Eric Lyn is grateful to ORNL for its hospitality during April–May, 1985